136 BUTLER ART. D 



temperature t by f4, lA and /jli. Let ^o be the freezing point of 

 the pure solvent and t, the freezing point of the solution. For 

 the equilibrium of the solid with the pure solvent at ^o it is 

 necessary that 



Z!2 = :^«, (173) 



and similarly for the equilibrium of the solution with the solid 

 at t, 



6 = ^« 

 t t' 



(174) 



By (161) 



so that 



din'jt) _ x; 





dt e 



ti' = ^- f'^-dt (175) 



t to J'o t^ . ^ ^ 



Similarly, for the pure solvent, we have 



7 = 7^- rS'^^ (176) 



t to Jto r 



and by (166), if Pi and pi are the partial vapor pressures of 

 Si over the liquid solvent and over the solution at t, and Af/°^ is 

 its molecular weight in the vapor, we have 



i = f + ji^'°s^''-/p'°'" 



so that 



T-'i-Lj-" + w^>'''^^^/^'°^'- <^"' 



Comparing (177) and (175), it is evident that 



^ \og{p,/p,^\= P^^--^-dt. (178) 



Mi^^^ 



